In FIG. 1, the structure of a conventional modulator 10 for polarization-division multiplexed (PDM) signals is shown. The modulator 10 of FIG. 1 is devised for PDM quadrature amplitude modulation (QAM). The modulator 10 comprises a first dual parallel Mach-Zehnder-modulator modulator (DP-MZM) 12, which comprises an input 14 for inputting an optical carrier, and an output 16 for outputting a QAM-modulated signal associated with a first polarization, which is referred to as “H-polarization” component in the following. Downstream of the optical input 14, the DP-MZM 12 branches into a first and a second arm 18, 20, respectively, that are rejoined at the optical output 16, thereby forming what is referred to as an “outer MZM” in the present disclosure.
Within each of the first and second arms 18, 20 of the outer MZM, respective first and second “inner” MZMs 22, 24 are provided. The first inner MZM 22 comprises electrodes (not shown) for applying a first driving voltage VHI for generating an in-phase component sHI of the H-polarization of the optical signal to be transmitted. In other words, the first driving voltage VHI is intended for modulating the part of the carrier signal propagating along the first arm 18 of the outer MZM according to the I-component of the base band signal. Likewise, electrodes (not shown) are associated with the second inner MZM 24, for applying a second driving voltage VHQ for generating a quadrature component sHQ of the H-polarization component of the optical signal. In the second arm 20, a first phase shifter 26 is provided in order to introduce the desired shift by 90° between the in-phase and quadrature components sHI and sHQ of the modulated signal before the I- and Q-modulated signals are combined at the optical output 16.
The modulator 10 further comprises a second DP-MZM 28 which is of similar structure as the first DP-MZM 12 and likewise comprises an optical input 14, which is identical to the optical input of the first DP-MZM 12, an optical output 30, and third and fourth arms 32, 34 including third and fourth inner MZMs 36 and 38, respectively. In the fourth arm 34, a further 90° phase shifter 40 is provided. Downstream of the optical output 30 of the second DP-MZM 28, a transverse-electric-/transverse-magnetic polarization mode converter 42 is provided, which polarizes the light outputted at the output 30 to a second polarization, referred to as the “V-polarization” hereinafter, wherein the H- and V-polarizations are orthogonal to each other. The third and fourth inner MZMs 36, 38 each have electrodes (not shown) for applying third and fourth driving voltages VVI and VVQ, respectively, for generating in-phase and quadrature components sVI and sVQ, respectively of the V-polarization component of the optical signal to be transmitted. The two orthogonally polarized optical signals are combined at a polarization beam splitter/combiner (PBS) 44 for outputting the combined signal. Since this combined signal comprises two mutually orthogonal polarization components H and V, the transmission method is referred to as a “polarization division multiplexing” (PDM).
Each of the first through fourth inner MZMs 22, 24, 36, 38 exhibits a periodic, theoretically sinusoidal transfer function (see FIG. 2) between the respective driving voltage (i.e. VHI, VHQ, VVI or VVQ) and the amplitude of the output electrical field component of the optical signal in the respective arm 18, 20, 32, 34 of the respective DP-MZM 12, 28. As shown in FIG. 2, to ensure a one-to-one correspondence between input and output, the inner MZMs 22, 24, 36, 38 are driven over a voltage swing region that does at least not exceed half a period of the transfer function. The swing of the driving voltage is typically centered on a biasing point, which for proper operation should lie at or at least near a zero-crossing of the transfer function. FIG. 2 shows two possible biasing points A and B with a respective swing of the driving voltage. Since the driving voltage aims at modulating an optical signal, it may also be referred to as “modulating voltage” herein.
In the art, several bias control algorithms are known to automatically adjust the bias voltage and to track the drift of the transfer function over temperature and time, such as the bias control algorithms disclosed in P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-loop bias control of optical quadrature modulator,” IEEE Photonics Technology Letters, vol. 18, no. 21, pp. 2209-2211, November 2006 and M. Sotoodeh, Y. Beaulieu, J. Harley, and D. L. McGhan, “Modulator bias and optical power control of optical complex E-field modulators,” IEEE Journal of Lightwave Technology, vol. 29, no. 15, pp. 2235-2248, August 2011. These prior art bias control algorithms monitor the optical output of each respective MZM via a photo diode. However, due to the quadratical characteristics of the employed photo-detectors, these algorithms cannot discern between bias points with negative transfer function slope, such as bias point A in FIG. 2, and bias points with positive transfer function slope, as is the case for bias point B in FIG. 2, thereby leading to an uncertainty in the sign of the actual transfer function.
For the sake of exemplification, let us first consider the H-polarization only, and assume that the equivalent complex base band representation of the intended QAM signal issH=sHI+j·sHQ,  (1)where j denotes the imaginary part of the complex number. It is further assumed that the biasing point of both inner MZMs 22, 24 has a positive slope, and that the optical fields sHI and sHQ are due to corresponding control voltages VHI, VHQ, respectively. If, however, the actual biasing points should both have a negative slope, for the same control voltages VHI and VHQ, the H-polarization component of the optical signal S′H, again in its complex base band representation would turn out to bes′H=−sHI−j·sHQ.  (2)
This signal s′H is congruent with sH, except for a rotation by 180°. Accordingly, the uncertainty in the sign of the transfer function would combine with the uncertainty of the absolute channel phase over the entire optical channel, which can be seamlessly compensated during the demodulation process at the receiver side without impact on the data transmission.
However, if the slopes of the transfer functions for the HI and HQ components should have opposite signs, the resulting signal exhibits, along with a possible rotation, also a complex conjugation, which in the frequency domain corresponds to a so-called “spectral inversion” around the carrier frequency. For example, if the transfer function for the HI-component (i.e. of the first inner MZM 22) should have a positive slope at the bias point, while the transfer function of the HQ-component (i.e. of the second inner MZM 24) should have a negative slope, the actual transmit signal s″H, i.e. the optical signal at the output 16 of the first DP-MZM 12 for the same driving voltages VHI and VHQ would turn out to bes″H=−sHI+j·sHQ=−s*H,  (3)which is a rotated and complex conjugated version of the intended signal sH.
The phenomenon of spectral inversion is for example described in E. Jacobsen, “Handling Spectral Inversion in Baseband Processing,” http://www.dsprelated.com/showarticle/51.php Feb. 11, 2008. A compensation method for such spectral inversion for the case of radio systems is described in I. Horowitz, M. Ben-Ayun; E. Fogel, “A radio device with spectral inversion”, GB2282286 (B)—Dec. 17, 1997.
In the case of so-called “blind” or “non-data aided” optical transmission, it is known to correct the spectral inversion at the receiver after complete demodulation. This is for example described in M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “DSP for Coherent Single-Carrier Receivers,” Journal of Lightwave Technology, Vol. 27, No. 16, Aug. 15, 2009, pp. 3614-3622. This is possible, because practical symbol constellations possess reflection symmetries through the origin of the IQ-plane and are therefore invariant under complex conjugation. Accordingly, a spectral inversion at the MZMs transforms the intended transmit signal into another valid transmit signal that is based upon the same symbol constellation and exhibits the same statistical properties. Accordingly, a blind demodulation process can be applied without any modification to the spectrally inverted signal. After demodulation, the recovered—and possibly complex conjugated—noisy symbols can then be de-mapped to hard-decided bits, or in the case of soft-decision forward error correction (EFC), to soft bits. At this stage the spectral inversion can then be detected and corrected. For this purpose, one can for example take advantage of the fact that, generally, the bit stream is organized in a frame structure with a unique word (UW) marking the beginning of each frame. The frame detector may continuously search for the periodic UW and raise a frame loss signal if it is unable to find it. This alarm can be used to trigger the correction of the spectral inversion, which can in this case be simply implemented via complex conjugation of the demodulated symbols before demapping.
The case of data-aided optical transmission, as for example described in M. Kuschnerov, M. Chouayakh, K. Piyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. S. Alfiad, A. Napoli, B. Lankl, “Data-Aided Versus Blind Single-Carrier Coherent Receivers,” IEEE Photonics Journal, Vol. 2, No. 3, June 2010, pp. 386-403, poses more difficult challenges. In data-aided transmission, the modulator embeds training sequences and/or reference symbols into the transmit signal, and the demodulator exploits them to estimate the parameters necessary for proper demodulation, such as the channel response and the frequency and phase difference between transmit and receive lasers. Contrary to the symbol constellation, such training sequences and reference symbols are not invariant under complex conjugation. Therefore, in the case of data-aided transmission, spectral inversion would have to be corrected before data-aided demodulation. One possible solution for this could be similar to the solution described above for blind transmission: Spectral inversion could be detected at the receiver by searching for the training sequences or the reference symbols, and corrected via complex conjugation of the received samples before the demodulation process, for example in a way described in U.S. Pat. No. 7,697,636 B2. However, for reasons explained in the following, this approach cannot be easily applied in data-aided optical PDM transmission, i.e. if the signal includes two polarization components carrying independent data.
The additional difficulty in PDM applications is due to the fact that data-aided channel estimation for PDM systems is preferably performed by means of mutually orthogonal training sequences transmitted over the H- and V-polarizations. Although, in principle, orthogonality could be achieved by transmitting the training sequence on H while muting V and thereafter on V while muting H, this would not be bandwidth efficient and would also produce strong variations of the transmit power, which is detrimental in view of the nonlinearity of optical channels. For this reason, in M. Kuschnerov, M. Chouayakh, K. Piyawanno, B. Spinnler, E. de Man, P. Kainzmaier, M. S. Alfiad, A. Napoli, B. Lankl, “Data-Aided Versus Blind Single-Carrier Coherent Receivers,” IEEE Photonics Journal, Vol. 2, No. 3, June 2010, pp. 386-403 it is recommended to transmit two orthogonal training sequences on H and V simultaneously. The two training sequences can for example be obtained via cyclic shift from a single repeated Constant-Amplitude Zero-Auto-Correlation (CAZAC) sequence.
If the H and V transmit signals are both generated with the correct polarity, or both spectrally inverted, the orthogonality of the training sequences is preserved, because if the two original sequences are orthogonal, the complex conjugated sequences are mutually orthogonal too. However, if one and only one polarization, i.e. H or V, is spectrally inverted, the orthogonality between the transmitted training sequences is lost. This situation is referred to as “inconsistent spectral polarity” in the following. Since in this case the H and V component of the signal are mixed, they cannot be individually complex conjugated before demodulation, but would rather have to be corrected at the transmitter. For PDM data-aided transmission, it would hence appear necessary to detect spectral inversion at the receiver by comparing the received signals with the expected training sequences, and to then correct the spectral inversion at the transmitter. This possible approach would hence require a backward channel from the receiver to the transmitter and suffers from a bootstrapping difficulty.